1. I am sure that she was angry with him.

Question

2. I am sure she was angry with him.
3. I am certain that she was angry with him.
4. It is sure/certain that he was pleased with the gift.
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Can we use both 'sure' and 'certain' in the sentences? In Sentence 4, the 'that clause' is a noun clause. Then, what about the 'that clause' in Sentences 1 and 3? A noun clause or an adverbial clause?

Answer 1

Yes, "sure" and "certain" mean the same thing here.

In these sentences, "that" is a subordinating conjunction, I think. Another tutor may correct me!
http://grammar.ccc.commnet.edu/grammar/conjunctions.htm#subordinating_conjunctions
and
http://grammar.ccc.commnet.edu/grammar/conjunctions.htm#that